Fundamentals of Coulostatic Analysis Experimental Results for the Range of
lom5to lo-' Mole per Liter
PAUL DELAHAY and YASUSHI IDE Coates Chemical laboratory, louisiana State University, Baton Rouge, l a .
b Previously reported theory of coulostatic analysis is verified experimentally for the hanging mercury drop in the range of 10-5 to 10-7 mole per liter. Additional material on theory includes a three-dimensional plot for discussion of decay curves, introduction of a decay constant similar to the polarographic diffusion current constant, and correlation of these two constants. Experimental results are given for zinc and iodate ions and mixtures containing cadmium and zinc. Lowering of sensitivity to the level of 10-3 to 10-4 mole per liter b y a capacitor in parallel with the cell is demonstrated. The influence of the cell resistance up to 0.3 megohm and possibly higher appears to b e negligible. The method is suitable for analysis down to the level of 10-7 mole per liter and lends itself to the use of direct-reading instruments. Some further developments are indicated.
HE principle of a new electroanalytical method-the coulostatic method-was recently reported (S),and a detailed theoretical treatment was given ( I ) . I t was shown that the coulostatic method should prove most useful in the range of to lo-' mole per liter and that analysis should be feasible for any substance that can be determined, a t higher concentrations, by polarography with the dropping mercury electrode or voltammetry with a solid electrode. Experimental results which substantiate this claim and the previously developed theory are reported here for the hanging mercury drop. The principle of the method is discussed first on the basis of a threedimensional plot similar to those for other analytical methods (9, IO), and practical methods for the analysis of data are introduced.
THEORY
Three-Dimensional Plot a n d Basic Equations. Consider a plane electrode on which a substance is reduced or
oxidized with mass transfer controlled by semi-infinite linear diffusion. The 1580
ANALYTICAL CHEMISTRY
A'
Figure 1 . Three-dimensional plot for interpretation of coulostatic analysis
E-t plane represents the decay of potential during double layer discharge. Equations for the E-t variations were derived (1: 3) for different types of electrodes and varied electrolysis conditions. Only two of these results cerresponding to the following conditions are needed here: plane electrode n-ith mass transfer controlled by semi-infinite linear diffusion, decay of potential in the diffusion current range, double layer capacity independent of potential; and the same conditions except for use of a spherical electrode with mass transfer controlled by diffusion toward the electrode in an infinite volume of solution. The corresponding potential-time relationships are :
diffusion current density, I d , is independent of potential and is given by I d =
T
c
P
nFCO
(,>I"
The diffusion current-potential-time relationship is represented in a threedimensional diagram (Figure 1) by a cylindric surface, normal to the I-t plane, whose intersection with the I-t plane is given by Equation 1. Assume that the electrode potential has initially a value a t which the faradaic current density is practically equal to zero. The charge on the electrode is suddenly varied by the flow of a short current pulse-e.g., of microsecond durationof such magnitude that the potential is now in the diffusion current range. Design of the pulse generator is such that the cell circuit is open, and the faradaic current subsequent to charging of the electrode is entirely supplied by discharge of the double layer capacity. As a result, the potential decays continuously toward positive or negative values (IUPAC-Stockholm Convention) for a net cathodic or anodic process, respectively, until it reaches a value a t which no faradaic process oecurs. The potential decays along curve CD on the cylindric surface, ABB'A', of Figure 1, provided the decay of potential is limited to the diffusion current range. The projection, GF, of this curve on the
The units in Equations 2 and 3 are: AE in volts, F in coulombs, c in microfarads per square centimeter, D in square centimeters per second, Co in moles per cubic centimeter, r in centimeters, and tin seconds. The i sign in Equations 2 and 3 corresponds to a net cathodic or anodic electrode process, respectively. These equations show that the shift of potential AE a t time t during decay is proportional to the bulk concentration, Co,of the substance being reduced or oxidized. Decay Constant. It is convenient to introduce by analogy with the diffusion current constant of classical polarography a decay constant. A, defined by
This decay constant is characteristic of a substance for reduction or oxidation under given electrolysis conditions (supporting electrolyte concentration, temperature, etc.). Equations 2 and 3 can then be written in a form which includes only quantities varying from one experiment to another. Thus, ztAE = X
CO
-
t"'
(5)
10-6
A2
co t
nrc
(6)
The decay constant is readily correlated to the polarographic diffusion current constant, I
